Liquid crystalline phases of matter often exhibit visually stunning patterns or textures. Mostly, these liquid crystal (LC) configurations are uniquely determined by bulk LC elasticity, surface anchoring conditions, and confinement geometry. Here, we experimentally explore defect textures of the smectic LC phase in unique confining geometries with variable curvature. We show that a complex range of director configurations can arise from a single system, depending on sample processing procedures. Specifically, we report on LC textures in Janus drops comprised of silicone oil and 8CB in its smectic-A LC phase. The Janus droplets were made in aqueous suspension using solvent-induced phase separation. After drop creation, smectic layers form in the LC compartment, but their self-assembly is frustrated by the need to accommodate both the bowl-shaped cavity geometry and homeotropic (perpendicular) anchoring conditions at boundaries. A variety of stable and metastable smectic textures arise, including focal conic domains, dislocation rings, and undulations. We experimentally characterize their stabilities and follow their spatiotemporal evolution. Overall, a range of fabrication kinetics produce very different intermediate and final states. The observations elucidate assembly mechanisms and suggest new routes for fabrication of complex soft material structures in Janus drops and other confinement geometries.
more »
« less
Phase-field model for a weakly compressible soft layered material: morphological transitions on smectic–isotropic interfaces
A coupled phase-field and hydrodynamic model is introduced to describe a two-phase, weakly compressible smectic (layered phase) in contact with an isotropic fluid of different density. A non-conserved smectic order parameter is coupled to a conserved mass density in order to accommodate non-solenoidal flows near the smectic–isotropic boundary arising from density contrast between the two phases. The model aims to describe morphological transitions in smectic thin films under heat treatment, in which arrays of focal conic defects evolve into conical pyramids and concentric rings through curvature dependent evaporation of smectic layers. The model leads to an extended thermodynamic relation at a curved surface that includes its Gaussian curvature, non-classical stresses at the boundary and flows arising from density gradients. The temporal evolution given by the model conserves the overall mass of the liquid crystal while still allowing for the modulated smectic structure to grow or shrink. A numerical solution of the governing equations reveals that pyramidal domains are sculpted at the center of focal conics upon a temperature increase, which display tangential flows at their surface. Other cases investigated include the possible coalescence of two cylindrical stacks of smectic layers, formation of droplets, and the interactions between focal conic domains through flow.
more »
« less
- Award ID(s):
- 1838977
- NSF-PAR ID:
- 10293559
- Date Published:
- Journal Name:
- Soft Matter
- Volume:
- 17
- Issue:
- 25
- ISSN:
- 1744-683X
- Page Range / eLocation ID:
- 6140 to 6159
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
The present work uses a reduced-order model to study the motion of a buoyant vortex ring with non-negligible core size. Buoyancy is considered in both non-Boussinesq and Boussinesq situations using an axisymmetric contour dynamics formulation. The density of the vortex ring differs from that of the ambient fluid, and both densities are constant and conserved. The motion of the ring is calculated by following the boundary of the vortex core, which is also the interface between the two densities. The velocity of the contour comes from a combination of a specific continuous vorticity distribution within its core and a vortex sheet on the core boundary. An evolution equation for the vortex sheet is derived from the Euler equation, which simplifies considerably in the Boussinesq limit. Numerical solutions for the coupled integro-differential equations are obtained. The dynamics of the vortex sheet and the formation of two possible singularities, including singularities in the curvature and the shock-like profile of the vortex sheet strength, are discussed. Three dimensionless groups, the Atwood, Froude and Weber numbers, are introduced to measure the importance of physical effects acting on the motion of a buoyant vortex ring.more » « less
-
more » « less
Abstract We present a phase-field (PF) model to simulate the microstructure evolution occurring in polycrystalline materials with a variation in the intra-granular dislocation density. The model accounts for two mechanisms that lead to the grain boundary migration: the driving force due to capillarity and that due to the stored energy arising from a spatially varying dislocation density. In addition to the order parameters that distinguish regions occupied by different grains, we introduce dislocation density fields that describe spatial variation of the dislocation density. We assume that the dislocation density decays as a function of the distance the grain boundary has migrated. To demonstrate and parameterize the model, we simulate microstructure evolution in two dimensions, for which the initial microstructure is based on real-time experimental data. Additionally, we applied the model to study the effect of a cyclic heat treatment (CHT) on the microstructure evolution. Specifically, we simulated stored-energy-driven grain growth during three thermal cycles, as well as grain growth without stored energy that serves as a baseline for comparison. We showed that the microstructure evolution proceeded much faster when the stored energy was considered. A non-self-similar evolution was observed in this case, while a nearly self-similar evolution was found when the microstructure evolution is driven solely by capillarity. These results suggest a possible mechanism for the initiation of abnormal grain growth during CHT. Finally, we demonstrate an integrated experimental-computational workflow that utilizes the experimental measurements to inform the PF model and its parameterization, which provides a foundation for the development of future simulation tools capable of quantitative prediction of microstructure evolution during non-isothermal heat treatment.
-
BACKGROUND Landau’s Fermi liquid theory provides the bedrock on which our understanding of metals has developed over the past 65 years. Its basic premise is that the electrons transporting a current can be treated as “quasiparticles”—electron-like particles whose effective mass has been modified, typically through interactions with the atomic lattice and/or other electrons. For a long time, it seemed as though Landau’s theory could account for all the many-body interactions that exist inside a metal, even in the so-called heavy fermion systems whose quasiparticle mass can be up to three orders of magnitude heavier than the electron’s mass. Fermi liquid theory also lay the foundation for the first successful microscopic theory of superconductivity. In the past few decades, a number of new metallic systems have been discovered that violate this paradigm. The violation is most evident in the way that the electrical resistivity changes with temperature or magnetic field. In normal metals in which electrons are the charge carriers, the resistivity increases with increasing temperature but saturates, both at low temperatures (because the quantized lattice vibrations are frozen out) and at high temperatures (because the electron mean free path dips below the smallest scattering pathway defined by the lattice spacing). In “strange metals,” by contrast, no saturation occurs, implying that the quasiparticle description breaks down and electrons are no longer the primary charge carriers. When the particle picture breaks down, no local entity carries the current. ADVANCES A new classification of metallicity is not a purely academic exercise, however, as strange metals tend to be the high-temperature phase of some of the best superconductors available. Understanding high-temperature superconductivity stands as a grand challenge because its resolution is fundamentally rooted in the physics of strong interactions, a regime where electrons no longer move independently. Precisely what new emergent phenomena one obtains from the interactions that drive the electron dynamics above the temperature where they superconduct is one of the most urgent problems in physics, attracting the attention of condensed matter physicists as well as string theorists. One thing is clear in this regime: The particle picture breaks down. As particles and locality are typically related, the strange metal raises the distinct possibility that its resolution must abandon the basic building blocks of quantum theory. We review the experimental and theoretical studies that have shaped our current understanding of the emergent strongly interacting physics realized in a host of strange metals, with a special focus on their poster-child: the copper oxide high-temperature superconductors. Experiments are highlighted that attempt to link the phenomenon of nonsaturating resistivity to parameter-free universal physics. A key experimental observation in such materials is that removing a single electron affects the spectrum at all energy scales, not just the low-energy sector as in a Fermi liquid. It is observations of this sort that reinforce the breakdown of the single-particle concept. On the theoretical side, the modern accounts that borrow from the conjecture that strongly interacting physics is really about gravity are discussed extensively, as they have been the most successful thus far in describing the range of physics displayed by strange metals. The foray into gravity models is not just a pipe dream because in such constructions, no particle interpretation is given to the charge density. As the breakdown of the independent-particle picture is central to the strange metal, the gravity constructions are a natural tool to make progress on this problem. Possible experimental tests of this conjecture are also outlined. OUTLOOK As more strange metals emerge and their physical properties come under the scrutiny of the vast array of experimental probes now at our disposal, their mysteries will be revealed and their commonalities and differences cataloged. In so doing, we should be able to understand the universality of strange metal physics. At the same time, the anomalous nature of their superconducting state will become apparent, offering us hope that a new paradigm of pairing of non-quasiparticles will also be formalized. The correlation between the strength of the linear-in-temperature resistivity in cuprate strange metals and their corresponding superfluid density, as revealed here, certainly hints at a fundamental link between the nature of strange metallicity and superconductivity in the cuprates. And as the gravity-inspired theories mature and overcome the challenge of projecting their powerful mathematical machinery onto the appropriate crystallographic lattice, so too will we hope to build with confidence a complete theory of strange metals as they emerge from the horizon of a black hole. Curved spacetime with a black hole in its interior and the strange metal arising on the boundary. This picture is based on the string theory gauge-gravity duality conjecture by J. Maldacena, which states that some strongly interacting quantum mechanical systems can be studied by replacing them with classical gravity in a spacetime in one higher dimension. The conjecture was made possible by thinking about some of the fundamental components of string theory, namely D-branes (the horseshoe-shaped object terminating on a flat surface in the interior of the spacetime). A key surprise of this conjecture is that aspects of condensed matter systems in which the electrons interact strongly—such as strange metals—can be studied using gravity.more » « less
-
Inspired by the recent realization of a two-dimensional (2-D) chiral fluid as an active monolayer droplet moving atop a 3-D Stokesian fluid, we formulate mathematically its free-boundary dynamics. The surface droplet is described as a general 2-D linear, incompressible and isotropic fluid, having a viscous shear stress, an active chiral driving stress and a Hall stress allowed by the lack of time-reversal symmetry. The droplet interacts with itself through its driven internal mechanics and by driving flows in the underlying 3-D Stokes phase. We pose the dynamics as the solution to a singular integral–differential equation, over the droplet surface, using the mapping from surface stress to surface velocity for the 3-D Stokes equations. Specializing to the case of axisymmetric droplets, exact representations for the chiral surface flow are given in terms of solutions to a singular integral equation, solved using both analytical and numerical techniques. For a disc-shaped monolayer, we additionally employ a semi-analytical solution that hinges on an orthogonal basis of Bessel functions and allows for efficient computation of the monolayer velocity field, which ranges from a nearly solid-body rotation to a unidirectional edge current, depending on the subphase depth and the Saffman–Delbrück length. Except in the near-wall limit, these solutions have divergent surface shear stresses at droplet boundaries, a signature of systems with codimension-one domains embedded in a 3-D medium. We further investigate the effect of a Hall viscosity, which couples radial and transverse surface velocity components, on the dynamics of a closing cavity. Hall stresses are seen to drive inward radial motion, even in the absence of edge tension.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/D1SM00488C
